OFFSET
0,2
COMMENTS
Arrange Pascal's triangle as a square array. This sequence is then a diagonal staircase on the square array.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = binomial(ceiling((n)/2) + n, n).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1, k). - Paul Barry, Jul 06 2004
Conjecture: 4*n*(n+1)*(6*n^2 - 15*n + 8)*a(n) + 6*n*(9*n-7)*a(n-1) - 3*(3*n-4)*(3*n-2)*(6*n^2-3*n-1)*a(n-2) = 0. - R. J. Mathar, Nov 07 2014
Conjecture: 8*n^2*(n+1)*a(n) - 12*n*(83*n^2 - 313*n + 232)*a(n-1) + 6*(-9*n^3 - 377*n + 384)*a(n-2) + 9*(3*n-5)*(83*n-64)*(3*n-7)*a(n-3) = 0. - R. J. Mathar, Nov 07 2014
MATHEMATICA
Table[Binomial[Ceiling[(n)/2] + n, n], {n, 0, 30}] (* Vincenzo Librandi, Aug 07 2013 *)
PROG
(Magma) [Binomial(Ceiling((n)/2) + n, n): n in [0..30]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved